Recently, [1]} suggested an alternative strategy to enable parallel computation.
Similar to the prox-linear method [2]}, it proposes to linearize around the previous iterate the quadratic penalty term in the augmented Lagrangian function, which makes the latter decomposable with respect to the \(x\)  blocks.
Although the method is shown to asymptotically converge for (REF ) (no convergence rate type is provided), it can be slow to converge in practice for models with highly nonconvex constraints.
Indeed, that analysis suggests an augmented Lagrangian penalty parameter that scales as \(O(\theta ^4)\)  posing numerical challenges.
Empirically, that method failed to converge for the smallest of our test instances with \(T = 3\) .
